Question

Lana is trying to find an equation for a line that passes through (5, 2) and is parallel to 3x + 2y = 15. Explain the steps that Lana could take to determine the equation. A) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the slope of that line and the point (5,2) into the point-slope formula. B) C) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the reciprocal of the slope of that line and the point (5,2) into the point-slope formula. Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5,2) into the point-slope formula. Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (0, 0) into the point-slope formula. D)

Answer 1

3x + 2y = 15

Make y the subject of the formula to make it in the slope-intercept form

`\begin{gathered} 2y=-3x+15 \\ \text{divide through all elements by 2} \\ (2y)/(2)=-(3x)/(2)+(15)/(2) \\ y=-1.5x+7.5 \end{gathered}`

The gradient of a line & the one parallel to it are equal:

Express the equation in general form