Slope and y-intercept

Correct answer: A. 6

In the form y=mx+c, the coefficient of x, m, is the slope. In y=6x+2, m=6, so the slope is 6. The number 2 is the y-intercept, not the slope. Exam tip: identify the coefficient of x to find the slope.

Correct answer: B. -5

In the form (y=mx+c), the constant term (c) is the (y)-intercept because putting (x=0) gives (y=c). Here, in (y=7x-5), (c=-5), so the (y)-intercept is -5. The number 7 is the slope, not the intercept. Exam tip: To find the (y)-intercept, put (x=0) in the equation.

Correct answer: A. The line crosses the y-axis at −2 and has slope 3.

In \(y=mx+c\), \(m\) is the slope and \(c\) is the y-intercept. Here \(m=3\) and \(c=-2\). Substituting \(x=0\) gives \(y=-2\). Exam tip: set \(x=0\) to find the y-intercept.

Correct answer: D. -5

The slope-intercept form of a line is y=mx+c, where the coefficient of x, m, is the slope. Here, y=13-5x can be written as y=-5x+13, so the slope is -5. The number 13 is the y-intercept, not the slope. Exam tip: To find the slope, identify the coefficient of x in the equation written as y=mx+c.

Correct answer: A. 11

To find the y-intercept, put x=0. In y=3x+11, substituting x=0 gives y=3(0)+11=11. Therefore, the y-intercept is 11, and the line meets the y-axis at (0, 11). Option 3 is the slope, not the y-intercept. Exam tip: in the form y=mx+c, c is always the y-intercept.

Correct answer: B. \(-9\)

A line in the form \(y=mx+c\) has slope \(m\). In \(y=-9x+4\), the coefficient of \(x\) is \(-9\), so the slope is \(-9\). The number \(4\) is the y-intercept, not the slope. Exam tip: In \(y=mx+c\), identify the coefficient of \(x\) to find the slope.

Correct answer: C. 8

The line y=8 is a horizontal line, so the value of y remains 8 for every value of x. To find the y-intercept, put x=0; the point obtained is (0, 8). Hence, the y-intercept is 8. It would be -8 only for the equation y=-8. Exam tip: for a line of the form y=c, the y-intercept is always c.

Correct answer: A. 0

A line is written as y=mx+c, where the coefficient of x, m, is the slope. In y=0x+17, the coefficient of x is 0, so the slope is 0. The number 17 is the y-intercept, not the slope. Exam tip: every horizontal line of the form y=constant has slope 0.

Correct answer: C. \(y=8x+3\)

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. Substituting \(m=8\) and \(c=3\) gives \(y=8x+3\). Although \(y=8x-3\) has the correct slope, its \(y\)-intercept is \(-3\). Exam tip: in \(y=mx+c\), the coefficient of \(x\) is the slope and the constant term is the \(y\)-intercept.

Correct answer: D. \(y=-5x+6\)

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. Substituting \(m=-5\) and \(c=6\) gives \(y=-5x+6\). Option A has a y-intercept of 6, but its slope is \(+5\), not \(-5\). Exam tip: in \(y=mx+c\), the coefficient of \(x\) is the slope.

Correct answer: A. 0

A line in the form \(y=mx+c\) has \(c\) as its \(y\)-intercept. In \(y=12x+0\), the constant term is \(0\), so the \(y\)-intercept is 0 and the line passes through the origin \((0,0)\). The number \(12\) is the slope, not the \(y\)-intercept. Exam tip: in \(y=mx+c\), the constant term gives the \(y\)-intercept directly.

Correct answer: B. -11

The slope-intercept form of a line is y = mx + c, where m is the slope. In y = -11x - 2, the coefficient of x is -11, so the slope is -11. The number -2 is the y-intercept, not the slope. Exam tip: In y = mx + c, identify the coefficient of x to find the slope.

Correct answer: C. 19

Write the line in the form (y=mx+c): (y=7x+19). Here, the constant term is (c=19), so the (y)-intercept is 19. The value 7 is the slope of the line, not its (y)-intercept. Exam tip: set (x=0) to find the (y)-intercept.

Correct answer: D. Slope -6, y-intercept 24

Compare the equation with slope-intercept form \(y=mx+c\). The given line can be written as \(y=-6x+24\). Thus, the coefficient of \(x\), \(-6\), is the slope, and the constant term, \(24\), is the y-intercept. Option B has the correct intercept but misses the negative sign in the slope. Exam tip: In \(y=mx+c\), \(m\) is always the coefficient of \(x\).

Correct answer: A. Slope \(4\), \(y\)-intercept \(-10\)

A line in standard slope-intercept form is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. Comparing \(y=4x-10\) with this form gives \(m=4\) and \(c=-10\). Hence, option A is correct. In option B, the slope and the \(y\)-intercept have been interchanged. Exam tip: the coefficient of \(x\) gives the slope, while the constant term gives the \(y\)-intercept.

Correct answer: B. Slope -1, y-intercept 15

Use the governing slope-intercept form y = mx + c. In this form, the coefficient m of x is the slope, while the constant c is the y-intercept. In y = -x + 15, the coefficient of x is -1, so the slope is -1. The constant term is 15, meaning the graph meets the y-axis at the point (0, 15); hence the y-intercept is 15. Thus option B is correct. Option A swaps the roles of the coefficient and constant, option C loses the negative sign, and option D assigns incorrect values and signs. A quick check is that increasing x by 1 changes y by -1, confirming the slope, while putting x = 0 gives y = 15, confirming the intercept.

Correct answer: C. \(\frac{3}{5}\)

In the slope-intercept form \(y=mx+c\), \(m\), the coefficient of \(x\), is the slope. Here, \(m=\frac{3}{5}\), so the correct answer is \(\frac{3}{5}\). The number 7 is the y-intercept, not the slope. Exam tip: in \(y=mx+c\), identify the number multiplying \(x\) to find the slope.

Correct answer: B. \(-4\)

A line in the form \(y=mx+c\) has y-intercept \(c\). Here, \(c=-4\), so the y-intercept is \(-4\). The value \(-\frac{7}{8}\) is the coefficient of \(x\), so it is the slope, not the y-intercept. Exam tip: put \(x=0\) to find the y-intercept.

Correct answer: A. Increases

A positive slope means that the line rises as we move from left to right. Therefore, when (x) increases, (y) also increases. “Remains constant” describes a horizontal line with zero slope, not a line with positive slope. Exam tip: If a graph rises from left to right, its slope is positive.

Correct answer: B. Decreases

A negative slope means that as the value of x increases, the value of y decreases. Therefore, the line moves downward from left to right. If y remains constant, the slope is 0, not negative. Exam tip: A line that falls from left to right has a negative slope.

Correct answer: A. The initial charge is 15, because \(y=15\) when \(x=0\).

The initial charge is the fare when distance is zero. Substituting \(x=0\) gives \(y=4(0)+15=15\). Here 4 is the slope, not the initial charge. Exam tip: the constant term is the y-intercept.

Correct answer: B. (0,10)

At any point on the y-axis, the value of x is 0. Substituting x=0 in y=-7x+10 gives y=10. Therefore, the line cuts the y-axis at (0,10). The value -7 is the slope, not the y-intercept. Exam tip: To find the y-intercept, always put x=0.

Correct answer: C. 9

In the form y=mx+c, m is the slope. Here, the coefficient of x is 9, so when x increases by 1, y increases by 9. The number 8 is the y-intercept; it does not represent the rate of increase of y. Exam tip: in y=mx+c, the coefficient of x is the slope.

Correct answer: D. Decreases by (8)

The equation is in the form y = mx + c, where the coefficient of x, m, is the slope. Here the slope is -8, so an increase of 1 in x produces a change of -8 in y; that is, y decreases by 8. The number 21 is the y-intercept, not the rate of change. Exam tip: identify the coefficient of x to find the slope directly.

Correct answer: C. -13

The equation of the line is y=10x-13. The term 10x depends on x, whereas -13 has no x. Therefore, the constant term is -13. The number 13 is only its positive value, so it is not correct. Exam tip: A term without a variable is the constant term.