Question

On a coordinate plane, a line goes through (0, negative 1) and (3, 1). a point is at (negative 3, 0). what is the equation of the line that is parallel to the given line and has an x-intercept of –3? y = two-thirdsx 3 y = two-thirdsx 2 y = negative three-halvesx 3 y = –three-halvesx 2

Answer 1

Required Equation is $y = \frac{2x}{3}+2$

Given: A line passing through $({x}_1,{y}_1)$ and $({x}_2,{y}_2)$

Slope = $\frac{(y_2 - y_1)}{(x_2 - x_1)}$ = $\frac{( 1 - (-1))}{(3 - 0)}= \frac{2}{3}$

Equation of line is:

$Y_1(x) = \frac{2}{3}x + b$

Where b is y intercept

for value of b

$Y_1(0) = -1 = \frac{2}{3}*0 + b = b$

⇒ b = -1

and Equation of line is:

$Y_1(x) = \frac{2}{3}x + (-1)$

For another parallel line that passes through the point (-3,0)

$Y_2(x)= \frac{2}{3}x + c$

$Y_2(-3) = 0 = {2}{3}*-3 + c = -2 + c = 0$

c = 2

then the equation is:

$Y_2(x) = \frac{2}{3}x + 2$

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