Write an equation in slope-intercept form of the line that passes through the points (-3,4) and (7,6) .
A) $y = \frac { 1 } { 5 } x + \frac { 23 } { 5 }$
B) $y = \frac { 1 } { 5 } x + 6$
C) $y = 5 x - 37$
D) $y = - \frac { 1 } { 5 } x + \frac { 29 } { 5 }$

Question

Write an equation in slope-intercept form of the line that passes through the points (-3,4) and (7,6)  .
A) $y = \frac { 1 } { 5 } x + \frac { 23 } { 5 }$
B) $y = \frac { 1 } { 5 } x + 6$
C) $y = 5 x - 37$
D) $y = - \frac { 1 } { 5 } x + \frac { 29 } { 5 }$

Quizplus · Accepted Answer

First, calculate the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, which gives $m = \frac{6 - 4}{7 - (-3)} = \frac{2}{10} = \frac{1}{5}$. Then, use one of the points and the slope to find the y-intercept (b) using the formula $y = mx + b$. Substituting one of the points (-3,4) and the slope into the equation gives $4 = \frac{1}{5}(-3) + b$, solving for b gives $b = \frac{23}{5}$. Thus, the equation is $y = \frac{1}{5}x + \frac{23}{5}$.

Write an Equation in Slope-Intercept Form of the Line That y=15x+235y = \frac { 1 } { 5 } x + \frac { 23 } { 5 }y=51​x+523​

Write an Equation in Slope-Intercept Form of the Line That $y = \frac { 1 } { 5 } x + \frac { 23 } { 5 }$