Question

Indicate the equation of the given line in standard form. The line through (2, -1) and parallel to a line with slope of 3/4

Answer 1

Well, for a line with a slope of 3/4, any other parallel line to it, will also have the same slope of 3/4

so if the line through (2, -1) is parallel to it, it has a slope of 3/4 as well

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ -1}})\quad \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{4} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \begin{array}{llll} \textit{plug in the values for } \begin{cases} y_1=-1\\ x_1=2\\ m=\frac{3}{4} \end{cases}\\ \textit{and move everything}\\ \textit{to the left-hand-side} \end{array}\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}$