Linear equation from two points (SAT) Practice Questions (Grade 9)

Question 1easy

A line passes through the points $(0, -3)$ and $(4, 1)$ . Which equation represents this line in slope-intercept form?

The slope is $m = \dfrac{1 - (-3)}{4 - 0} = 1$ . Because the line passes through $(0, -3)$ , the $y$ -intercept is $b = -3$ where $x = 0$ . The equation is $y = x - 3$ .

Question 2medium

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

The slope is $m = \dfrac{4 - (-4)}{5 - 1} = 2$ . Substitute $(1, -4)$ : $-4 = 2(1) + b$ , so $b = -6$ . The equation is $y = 2x - 6$ .

Question 3medium

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

The slope is $m = \dfrac{-2 - 4}{2 - (-1)} = -2$ . Substitute $(-1, 4)$ : $4 = -2(-1) + b$ , so $b = 2$ . The equation is $y = -2x + 2$ .

Question 4medium

A line passes through the points $(2, 1)$ and $(6, 4)$ . Which equation represents this line in slope-intercept form?

The slope is $m = \dfrac{4 - 1}{6 - 2} = \dfrac{3}{4}$ . Substitute $(2, 1)$ : $1 = \dfrac{3}{4}(2) + b$ , so $b = -\dfrac{1}{2}$ . The equation is $y = \dfrac{3}{4}x - \dfrac{1}{2}$ .

Question 5medium

A line passes through the points $(-3, 0)$ and $(1, 4)$ . Which equation represents this line in slope-intercept form?

The slope is $m = \dfrac{4 - 0}{1 - (-3)} = 1$ . Substitute $(-3, 0)$ : $0 = 1(-3) + b$ , so $b = 3$ . The equation is $y = x + 3$ .

Question 6medium

A line passes through the points $(1, 2)$ and $(7, 5)$ . Which equation represents this line in slope-intercept form?

The slope is $m = \dfrac{5 - 2}{7 - 1} = \dfrac{1}{2}$ . Substitute $(1, 2)$ : $2 = \dfrac{1}{2}(1) + b$ , so $b = \dfrac{3}{2}$ . The equation is $y = \dfrac{1}{2}x + \dfrac{3}{2}$ .

Question 7medium

A line passes through the points $(-4, -1)$ and $(2, 5)$ . Which equation represents this line in slope-intercept form?

The slope is $m = \dfrac{5 - (-1)}{2 - (-4)} = 1$ . Substitute $(-4, -1)$ : $-1 = 1(-4) + b$ , so $b = 3$ . The equation is $y = x + 3$ .

Question 8medium

A line passes through the points $(2, -3)$ and $(6, 1)$ . Which equation represents this line in slope-intercept form?

The slope is $m = \dfrac{1 - (-3)}{6 - 2} = 1$ . Substitute $(2, -3)$ : $-3 = 1(2) + b$ , so $b = -5$ . The equation is $y = x - 5$ .

Linear equation from two points (SAT) practice

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