Digital PSAT Math Practice Question 261: Answer and Explanation

Question: 261

If a line has a slope of 3 and intersects the point (1, 8), what is the y-intercept of the line?

• A. 5
• B. 3
• C. -1
• D. -3

Correct Answer: A

Explanation:

(A) Plug the given slope and point coordinates into the point-slope equation: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) are the coordinates of a point on the line. Therefore,

y - 8 = 3(x - 1)

Next, distribute the 3:

y - 8 = 3x - 3

To get the line in slope-intercept form, add 8 to both sides:

y = 3x + 5. Therefore, the y-intercept is 5, choice (A). You could also plug 3 in for the slope and the point (1, 8) into the line when it is in slope-intercept form: y = mx + b. Then you could solve for the y-intercept b.