Slope and y-intercept

Correct answer: A. \((0,3)\)

The equation of the line is \(y=-4x+3\). Every point on the \(y\)-axis has \(x=0\). Substituting \(x=0\) gives \(y=-4(0)+3=3\), so the intercept is \((0,3)\). The point \((3,0)\) lies on the \(x\)-axis, not on the \(y\)-axis. Exam tip: in \(y=mx+c\), the \(y\)-intercept is \((0,c)\).

Correct answer: B. 10

The slope of the line y=10x+4 is 10. The slope tells how much y changes when x increases by 1 unit. Therefore, y increases by 10. The number 4 is the y-intercept, not the increase in y. Exam tip: In y=mx+c, the change in y for a unit change in x is m.

Correct answer: C. Decreases by 7

In the form y = mx + c, the coefficient of x, m, is the slope. Here the slope is -7, so an increase of 1 in x produces a change of -7 in y; therefore, y decreases by 7. The number 20 is the y-intercept, not the change in y. Exam tip: for a 1-unit increase in x, the change in y equals the slope.

Correct answer: C. -9

In y=4x-9, the term 4x depends on x, whereas -9 has no x. Therefore, the constant term is -9. Here, 4 is the coefficient of x, not the constant term. Exam tip: the term with no variable is the constant term.

Correct answer: D. -8

The given equation is y=-8x+13. The number multiplying x is -8, so the coefficient of x is -8. The number 13 is the constant term, not the coefficient of x. Exam tip: The number directly multiplied by a variable is its coefficient.

Correct answer: B. \(y=2x+5\)

In the form \(y=mx+c\), \(c\) is the \(y\)-intercept because substituting \(x=0\) gives \(y=c\). In \(y=2x+5\), the constant term is \(5\), so its \(y\)-intercept is \(5\). In \(y=5x+2\), \(5\) is the slope, not the \(y\)-intercept. Exam tip: To find the \(y\)-intercept, put \(x=0\) in the equation.

Correct answer: A. \(y=-4x+1\)

In the form \(y=mx+c\), the coefficient of \(x\), namely \(m\), is the slope. In \(y=-4x+1\), the coefficient of \(x\) is \(-4\), so its slope is \(-4\). The line \(y=-x+4\) has slope \(-1\), not \(-4\). Exam tip: In \(y=mx+c\), identify the slope by checking the signed coefficient of \(x\).

Correct answer: C. Slope −5, y-intercept 15

The slope-intercept form of a line is y = mx + c, where m is the slope and c is the y-intercept. Rewriting the given equation as y = −5x + 15 gives m = −5 and c = 15. Hence, option C is correct. In option B, the sign of the coefficient of x is incorrect. Exam tip: Always check the sign attached to the coefficient of x when finding the slope.

Correct answer: A. \(y=4x-3\)

In the form \(y=mx+c\), the constant term \(c\) is the \(y\)-intercept. In \(y=4x-3\), \(c=-3\). In \(y=-3x+4\), \(-3\) is the slope, not the intercept. Exam tip: identify the constant term.

Correct answer: A. Slope

In the slope-intercept form y=mx+c, m represents the slope of the line, that is, the change in y for a one-unit change in x. Here c=6, so 6 is the y-intercept, not m. The x-intercept is found where y=0. Exam tip: In y=mx+c, identify m as the slope and c as the y-intercept.

Correct answer: C. y-intercept of the line

In the form y=mx+c, m is the slope and c is the y-intercept. Here, putting x=0 gives y=c, so the line meets the y-axis at (0,c). The coefficient of x is 4, so it represents the slope, not c. Exam tip: To find the y-intercept, substitute x=0 in the equation.

Correct answer: D. -3

To find the y-intercept, put x=0. Then y=-0-3=-3. Thus, the line meets the y-axis at -3, so the correct answer is -3. The value -1 is the coefficient of x, not the y-intercept. Exam tip: in y=mx+c, c is the y-intercept.

Correct answer: A. 13

A line in the form \(y=mx+c\) has slope \(m\). In \(y=13x+8\), the coefficient of \(x\) is 13, so the slope is 13. The number 8 is the y-intercept, not the slope. Exam tip: In \(y=mx+c\), the coefficient of \(x\) is always the slope.

Correct answer: B. The point where the line intersects the y-axis

In \(y=mx+c\), putting \(x=0\) gives \(y=c\). Thus, the line meets the y-axis at \(c\), so \(c\) is the y-intercept. The coefficient \(m\), not \(c\), represents slope. Exam tip: set \(x=0\) to identify the y-intercept.

Correct answer: C. \(7\)

In the form \(y=mx+c\), \(c\) is the y-intercept, the y-coordinate where the line meets the y-axis. The given point is \((0,7)\), so \(c=7\). It would be \(-7\) only if the intercept were \((0,-7)\). Exam tip: every point on the y-axis has \(x=0\).

Correct answer: B. -2

In the form \(y=mx+c\), \(c\) is the y-intercept, meaning the value of \(y\) when \(x=0\). At the given point \((0,-2)\), \(y=-2\); therefore, \(c=-2\). Option \(2\) results from a sign error. Exam tip: in \(y=mx+c\), the y-intercept is directly \(c\).

Correct answer: A. \(y=6x-2\)

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. Substituting \(m=6\) and \(c=-2\) gives \(y=6x-2\). Option C has slope 6, but its \(y\)-intercept is \(+2\), so it is not correct. Exam tip: in \(y=mx+c\), the coefficient of \(x\) is the slope and the constant term is the \(y\)-intercept.

Correct answer: B. \(y=-x-5\)

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. Substituting \(m=-1\) and \(c=-5\) gives \(y=-x-5\). Option D has slope \(-1\), but its \(y\)-intercept is \(+5\). Exam tip: in \(y=mx+c\), the coefficient of \(x\) is the slope and the constant term is the \(y\)-intercept.

Correct answer: C. \(-4\)

A line in the form \(y=mx+c\) has y-intercept \(c\). Here, \(c=-4\), so the y-intercept is \(-4\). The value \(\frac{5}{3}\) is the slope, not the y-intercept. Exam tip: put \(x=0\) to find the y-intercept.

Correct answer: B. \(-\frac{2}{5}\)

A line in slope-intercept form is \(y=mx+c\), where \(m\) is the slope. In \(y=-\frac{2}{5}x+9\), the coefficient of \(x\) is \(-\frac{2}{5}\), so the slope is \(-\frac{2}{5}\). The number \(9\) is the y-intercept, not the slope, and \(\frac{2}{5}\) incorrectly omits the negative sign. Exam tip: in \(y=mx+c\), identify the coefficient of \(x\) as the slope.

Correct answer: C. 12

At every point on the (y)-axis, (x=0). Substituting (x=0) in (y=3x+12) gives (y=3(0)+12=12). Hence, the line cuts the (y)-axis at (y=12). Here, (3) is the slope, not the (y)-intercept. Exam tip: in the form (y=mx+c), (c) is always the (y)-intercept.

Correct answer: C. Negative

A line in the form y = mx + c has slope m, the coefficient of x. Here, m = -6, which is less than 0; therefore, the slope is negative. A zero slope would require the coefficient of x to be 0, as in y = 18. Exam tip: In y = mx + c, identify the slope by looking at the coefficient of x.

Correct answer: A. Positive

The slope-intercept form of a line is y=mx+c, where the coefficient of x, m, is the slope. Here m=11, and 11 is greater than zero, so the slope is positive. A negative slope would require the coefficient of x to be less than zero. Exam tip: In y=mx+c, identify the slope by looking at the coefficient of x.

Correct answer: A. Slope 0, y-intercept -10

A line written as y = mx + b has slope m and y-intercept b. Comparing y = 0x - 10 with this form gives m = 0 and b = -10. Thus the graph is a horizontal line crossing the y-axis at (0, -10). Option A states both values correctly. Option B interchanges the coefficient and constant, while options C and D incorrectly change the signs. The zero coefficient means there is no rise as x changes.

Correct answer: C. Coefficient -2, constant term 14

The given expression is (y=14-2x), which can be written in standard order as (y=-2x+14). The number multiplying (x) is -2, so the coefficient of (x) is -2. The term without (x) is 14; hence, the constant term is 14. In option B, the sign of the coefficient is incorrect. Exam tip: Always include the positive or negative sign with a coefficient.