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:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where:} \\ x_1,y_1\text{ are the coordinates of the point} \end{gathered}[/tex]
We therefore have:
[tex]\begin{gathered} y-3=2(x-4) \\ as\text{ our }point\text{ slope form} \end{gathered}[/tex]
Converting to slope-intercept form:
[tex]\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}[/tex]
