How do you write the equation in slope intercept form given (-5,0) and (3,3)?

Apr 12, 2017

See the entire solution process below:

Explanation:

First, we need to determine the slope for this equation. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{3} - \textcolor{b l u e}{0}}{\textcolor{red}{3} - \textcolor{b l u e}{- 5}} = \frac{\textcolor{red}{3} - \textcolor{b l u e}{0}}{\textcolor{red}{3} + \textcolor{b l u e}{5}} = \frac{3}{8}$

The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

We can substitute the slope we calculated and one of the points from the problem for $x$ and $y$ and solve for $b$:

$3 = \left(\textcolor{red}{\frac{3}{8}} \times 3\right) + \textcolor{b l u e}{b}$

$3 = \textcolor{red}{\frac{9}{8}} + \textcolor{b l u e}{b}$

$3 - \frac{9}{8} = - \frac{9}{8} + \textcolor{red}{\frac{9}{8}} + \textcolor{b l u e}{b}$

$\left(3 \times \frac{8}{8}\right) - \frac{9}{8} = 0 + \textcolor{b l u e}{b}$

$\frac{24}{8} - \frac{9}{8} = \textcolor{b l u e}{b}$

$\frac{15}{8} = \textcolor{b l u e}{b}$

Substituting this result and the slope we calculated into the formula gives:

$y = \textcolor{red}{\frac{3}{8}} x + \textcolor{b l u e}{\frac{15}{8}}$

Apr 12, 2017

The equation of the line in slope-intercept form is $y = \frac{3}{8} x + 1 \frac{7}{8}$

Explanation:

The slope of the line passing through $\left(- 5 , 0\right) \mathmr{and} \left(3 , 3\right)$ is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{3 - 0}{3 + 5} = \frac{3}{8}$

Let the equation of the line in slope-intercept form be $y = m x + c \mathmr{and} y = \frac{3}{8} x + c$ The point (-5,0) will satisfy the equation . So, $0 = \frac{3}{8} \cdot \left(- 5\right) + c \mathmr{and} c = \frac{15}{8} = 1 \frac{7}{8}$

Hence the equation of the line in slope-intercept form is $y = \frac{3}{8} x + 1 \frac{7}{8}$ graph{3/8x+15/8 [-10, 10, -5, 5]} [Ans]