Question

Use the information given to find the equation of the line using the point-slope formula (y-y_1)=m(x-x_1)). Then convert your answer to slope-intercept form (y=mx+b).Parallel to y=2x+5 and passes through the point (4,3)The point slope form is (y-Answer)=Answer(x-Answer)Converting it to slope intercept form gives us: y=Answerx+Answer

Answer 1

point-slopeWe are required to get the equation of the line in the point-slope and slope-intercept forms.

A line given in the form: y = mx + b is given in the slope-intercept form where m and b are the slope and intercept on the vertical axis respectively.

A pair of parallel lines have the same gradient and we will leverage this fact to get the equation of the line that passes through the point (4,3).

The point-slope slope form of a line is:

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where:} \\ x_1,y_1\text{ are the coordinates of the point} \end{gathered}`

We therefore have:

`\begin{gathered} y-3=2(x-4) \\ as\text{ our }point\text{ slope form} \end{gathered}`

Converting to slope-intercept form:

`\begin{gathered} y-3=2(x-4) \\ \text{Add 3 to both sides to get:} \\ y=2(x-4)+3 \\ y=2x-8+3 \\ y=2x-5 \end{gathered}`