The equation in point-slope form of the line that passes through the given points is [tex]y + 1 = \frac{6}{11}(x + 4)[/tex].
Given the following data:
- Points on the x-axis = (7, -4).
- Points on the y-axis = (5, -1).
To find the equation in point-slope form of the line that passes through the given points:
The slope of a line refers to the gradient of a line and it is typically used to describe both the direction and steepness of an equation of a straight line.
Mathematically, the slope of a line is given by the following formula;
[tex]Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Substituting the given points into the formula, we have;
[tex]Slope. \;m = \frac{-1 \;- \;5}{-4\; - \;7}\\\\Slope. \;m = \frac{-6}{-11}\\\\Slope. \;m = \frac{6}{11}[/tex]
To write the equation in point-slope form:
[tex]y - y_1 = m(x - x_1)\\\\y - (-1) = \frac{6}{11}(x - (-4))\\\\y + 1 = \frac{6}{11}(x + 4)[/tex]
Therefore, the equation in point-slope form of the line that passes through the given points is [tex]y + 1 = \frac{6}{11}(x + 4)[/tex].
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