The value of m is either -4 or 3 which is the slope of the straight line.
The general equation of a straight line is of the form y=mx +c where m is the slope of the line and c is the y-intercept.
Slope is defined as the inclination or gradient of the straight line with respect to the positive x-axis. The y-intercept is the co-ordinate where the graph passes the y-axis.
The given equation of the graph :
(y − 4) = m(x − 7)
Simplifying:
y = mx + 4 - 7m
So the slope of the line is m .
Now the line passes through (−1, −2) and (m, 10) .
Slope of the line = (10-(-2))÷(m-(-1)) = 12 / (m+1)
Therefore we can infer that :
12 / (m+1) = m
or, 12 = m² + m
or, m² + m -12 = 0
or, (m+4)(m-3)=0
Either m = -4 or m = 3
Hence the value of m is either -4 or 3.
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