Question

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-1,6) and parallel to x + 3y = 7.a) The equation of the line in slope-intercept form is.(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

Answer 1

Answer:

$y=\frac{1}{3}x+\frac{19}{3}$

Step-by-step explanation:

Linear equations are represented in slope-intercept form by the following equation:

$\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=\text{ y-intercept} \end{gathered}$

If the line is parallel to x+3y=7, it means they have the same slope. Then, the slope would be;

$\begin{gathered} x+3y=7 \\ y=\frac{x}{3}-\frac{7}{3} \\ \text{ Slope is the coefficient that goes with the ''x''} \\ \text{Slope}=\text{ }\frac{1}{3} \end{gathered}$

Then, to find the y-intercept of the equation, substitute the slope and the given point, solve for b:

$\begin{gathered} 6=\frac{1}{3}(-1)+b \\ b=6+\frac{1}{3} \\ b=\frac{19}{3} \end{gathered}$

Hence, the equation would be:

$y=\frac{1}{3}x+\frac{19}{3}$