Slope-point line equations Practice Questions (Grade 9)

Question 1easy

A line has slope $4$ and passes through the point $(-1, 2)$ . Which equation represents this line in point-slope form?

Point-slope form is $y - y_1 = m(x - x_1)$ . With $m = 4$ and $(x_1, y_1) = (-1, 2)$ , $y - 2 = 4(x - (-1))$ , which is $y - 2 = 4(x + 1)$ .

Question 2medium

A line has slope $\dfrac{3}{2}$ and passes through the point $(4, 1)$ . Which equation represents this line in slope-intercept form?

Slope-intercept form is $y = mx + b$ . Substitute $(4, 1)$ with $m = \dfrac{3}{2}$ : $1 = \dfrac{3}{2}(4) + b = 6 + b$ , so $b = -5$ . The equation is $y = \dfrac{3}{2}x - 5$ .

Question 3medium

A line has slope $-2$ and passes through the point $(5, -3)$ . Which equation represents this line in point-slope form?

Point-slope form is $y - y_1 = m(x - x_1)$ . With $m = -2$ and $(x_1, y_1) = (5, -3)$ , $y - (-3) = -2(x - 5)$ , which is $y + 3 = -2(x - 5)$ .

Question 4medium

A line has slope $-\dfrac{1}{2}$ and passes through the point $(6, 4)$ . Which equation represents this line in point-slope form?

Point-slope form is $y - y_1 = m(x - x_1)$ . With $m = -\dfrac{1}{2}$ and $(x_1, y_1) = (6, 4)$ , $y - 4 = -\dfrac{1}{2}(x - 6)$ .

Question 5medium

A line has slope $3$ and passes through the point $(2, 8)$ . Which equation represents this line in standard form?

Standard form is $Ax + By = C$ . First write slope-intercept form $y = mx + b$ : $8 = 3(2) + b$ gives $b = 2$ , so $y = 3x + 2$ . Rearranging gives $3x - y = -2$ .

Question 6medium

A line has slope $-4$ and passes through the point $(1, 5)$ . Which equation represents this line in standard form?

Standard form is $Ax + By = C$ . First write slope-intercept form $y = mx + b$ : $5 = -4(1) + b$ gives $b = 9$ , so $y = -4x + 9$ . Rearranging gives $4x + y = 9$ .

Question 7medium

A line has slope $\dfrac{5}{4}$ and passes through the point $(-4, 3)$ . Which equation represents this line in point-slope form?

Point-slope form is $y - y_1 = m(x - x_1)$ . With $m = \dfrac{5}{4}$ and $(x_1, y_1) = (-4, 3)$ , $y - 3 = \dfrac{5}{4}(x - (-4))$ , which is $y - 3 = \dfrac{5}{4}(x + 4)$ .

Question 8hard

A line has slope $\dfrac{2}{3}$ and passes through the point $(9, 10)$ . Which equation represents this line in standard form?

Standard form is $Ax + By = C$ . First write slope-intercept form $y = mx + b$ : $10 = \dfrac{2}{3}(9) + b$ gives $b = 4$ , so $y = \dfrac{2}{3}x + 4$ . Multiply by $3$ : $3y = 2x + 12$ , so $-2x + 3y = 12$ .

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