Slope and y-intercept

A line with a positive slope rises from left to right. Therefore, as (x) increases, (y) generally increases. Option A describes a negative slope, while option D applies to a horizontal line with zero slope. Exam tip: a line that moves upward from left to right has a positive slope.

A line with a negative slope goes downward as we move from left to right. Therefore, when (x) increases, the value of (y) decreases, so option C is correct. A constant value of (y) represents zero slope, not negative slope. Exam tip: If a graph falls as you move to the right, its slope is negative.

A line with slope 0 is horizontal and has the form \(y=c\), where \(c\) is a constant. Therefore, \(y=5\) has slope 0. The slopes of \(y=5x\), \(y=x+5\), and \(y=-5x\) are 5, 1, and -5 respectively. Exam tip: In \(y=mx+c\), the coefficient of \(x\), namely \(m\), is the slope.

In the form \(y=mx+c\), \(c\) is the y-intercept. A line passes through the origin \((0,0)\) only when \(c=0\). In \(y=4x\), the constant term is 0, so substituting \(x=0\) gives \(y=0\). The other options have constant terms 2, −5, and 1, so they do not pass through the origin. Exam tip: test for the origin by substituting \(x=0\) and \(y=0\) in the equation.

Every point on the y-axis has x-coordinate 0. Substituting x=0 in y=2x+6 gives y=2(0)+6=6. Hence, the line cuts the y-axis at \((0,6)\). Although \((2,6)\) has y-coordinate 6, its x-coordinate is not 0, so it is not on the y-axis. Exam tip: To find the y-intercept, always put x=0.

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 \((0,c)\).

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.

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.

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.

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.

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.

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 \(x\).

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.

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.

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.

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.

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.

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.

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.

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 \(x=0\).