Answer:
D. [tex] y - 5= 3(x - 1) [/tex]
B. [tex] y = \frac{3}{2}x - 3 [/tex]
Step-by-step explanation:
Problem 1:
Point-slope form equation is given as [tex] y - y_1 = m(x - x_1) [/tex], where, (x1, y1) is a point on the line, and m = slope.
Find the slope of the line of the graph given, using 2 points on the line, points (0, 2) and (1, 5).
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 5}{0 - 1} = \frac{-3}{-1} = 3 [/tex]
Substitute (x1, y1) = (1, 5) and m = 3 into [tex] y - y_1 = m(x - x_1) [/tex]
[tex] y - 5= 3(x - 1) [/tex]
The answer is D.
Problem 2:
Slope-intercept equation takes the form: [tex] y = mx + b [/tex], where, m = slope, and b = y-intercept.
Find m and b.
Given, points (−4,−9) and (−2,−6),
[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 -(-9)}{-2 -(-4)} = \frac{3}{2} = \frac{3}{2} [/tex]
Substitute x = -2, y = -6, and m = ³/2 into [tex] y = mx + b [/tex], to find b:
[tex] -6 = \frac{3}{2}(-2) + b [/tex],
Subtract b from both sides
[tex] -6 = -3 + b [/tex]
Add 3 to both sides
[tex] -6 + 3 = b [/tex]
[tex] -3 = b [/tex]
[tex] b = -3 [/tex]
Substitute m = ³/2, b = -3 into [tex] y = mx + b [/tex]
[tex] y = \frac{3}{2}x + (-3) [/tex]
[tex] y = \frac{3}{2}x - 3 [/tex]
The answer is B.
