Find the equation of a line that contains the points (0,0) and (6,−7). Write the equation in slope-intercept form, using fractions when required.

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Question:

Find the equation of a line that contains the points (0,0) and (6,−7). Write the equation in slope-intercept form, using fractions when required.

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Use the slope formula below:[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]To form an equation of a line - we need to find a slope and the y-intercept from y = mx+b. We are given two points which we can substitute in the formula.[tex] \large{m = \frac{0 - ( - 7)}{0 - 6} } \\ \large{m = \frac{0 + 7}{ - 6} \longrightarrow \frac{7}{ - 6} } \\ \large \boxed{m = - \frac{7}{6} }[/tex]We have finally got the slope. Next is to find the y-intercept. First we rewrite the equation of y = mx+b by substituting the slope.[tex] \large \boxed{y = mx + b}[/tex]The equation above is the slope-intercept form. Substitute m = -7/6 in the equation.[tex] \large{y = - \frac{7}{6} x + b}[/tex]Since the graph passes through (0,0) which is an origin point. In y = mx+b if the graph passes through origin point, that means the b-value is 0. Therefore:[tex] \large \boxed{y = - \frac{7}{6} + 0 \longrightarrow y = - \frac{7}{6} x}[/tex]Answery = -7x/6Hope this helps and let me know if you have any doubts! Good luck on your assignment!

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