Question

find the equation of the line using the point slope formula. write the final equation using the slope intercept for thr x-intercept is 1 (x,y)=(-2,9) is a point on the line

Answer 1

we know the x-intercept of the line is 1, recall that an x-intercept is when the graph intercepts or touches the x-axis, and when that happens, y = 0, so the point is really x = 1, y = 0, namely (1,0). We also know another point on the line, is (-2, 9).

$\bf \stackrel{x-intercept}{(\stackrel{x_1}{1}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-0}{-2-1}\implies \cfrac{9}{-3}\implies -3 \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-0=-3(x-1) \\\\\\ ~\hspace{10em}y=-3x+3$