Writing Linear EquationsInstruction ActiveWriting an Equation Given Two Points on the LineWrite the equation of the line that passes through the points (7,-4) and (-1,3), first in point-slope form, and then inslope-intercept form.The slope of the line isWhen the point (7.-4) is used, the point-slope form of the line isThe slope-intercept form of the line is

Answer:[tex]\text{The slope:}\ m=-\dfrac{7}{8}\\\\\text{The point-slope form:}\ y+4=-\dfrac{7}{8}(x-7)\\\\\text{The slope-intercept form:}\ y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]Step-by-step explanation:The slope-intercept form of an equation of a line:[tex]y=mx+b[/tex]m - slopeb - y-interceptThe point-slope form of an equation of a line:[tex]y-y_1=m(x-x_1)[/tex]m - slopeThe formula of a slope:[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]We have two points (7, -4) amd (-1, 3).Calculate the slope:[tex]m=\dfrac{3-(-4)}{-1-7}=\dfrac{7}{-8}=-\dfrac{7}{8}[/tex]The point-slope form of an equation of a line:[tex]y-(-4)=-\dfrac{7}{8}(x-7)\\\\y+4=-\dfrac{7}{8}(x-7)[/tex]Convert to the slope-intercept form:[tex]y+4=-\dfrac{7}{8}(x-7)[/tex]        use the distributive property[tex]y+4=-\dfrac{7}{8}x+\dfrac{49}{8}[/tex]     subtract 4 = 32/8 from both sides[tex]y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]