Verified Answer :
I think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). Because if you replace x by -4 your are supposed to find y=-3 which is not the case her. If you replace x by -4 you find =-15.
I assume the right equation is y-1=1/4(x-12) because this one is passing through both your points (if you are interested to know how I found that out I can tell you).
In this equation if I replace x by -4 I find y=-3 and if I replace x by 12, I find y=1 so the line representing this equation is passing through those 2 points.
Then the standard form of the equation is finding an expression of y in function of x
y-1=1/4(x-12)
y=x/4-3+1
y=x/4-2
Hope that helps.
Do you confirm there was a mistake in the question?
The equation of line passes through points \(\left({ - \,4, - \,3}\right)\) and \(\left({12,1}\right)\) in standard form is \(\boxed{{\mathbf{x - 4y = 8 }}}\).
Further explanation:
It is given that a line passes through points \(\left({ - 4, - 3}\right)\) and \(\left({12,1}\right)\).
The slope of a line passes through points \(\left({{x_1},{y_1}}\right)\) and \(\left({{x_2},{y_2}}\right)\) is calculated as follows:
\(m=\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}{\text{ }}\) ......(1)
Here, the slope of a line is denoted as and points are \(\left({{x_1},{y_1}}\right)\) and \(\left({{x_2},{y_2}}\right)\).
Substitute for \({x_1}\) , \(-3\) for \({y_1}\) , \(12\) for \({x_2}\) and \(1\) for \({y_2}\) in equation (1) to obtain the slope of a line that passes through points \(\left({ - 4, - 3}\right)\) and \(\left({12,1}\right)\).
\(\begin{aligned}m&=\frac{{1 - \left({ - 3}\right)}}{{12 - \left({ - 4}\right)}}\\&=\frac{{1 + 3}}{{12 + 4}}\\&=\frac{4}{{16}}\\&=\frac{1}{4}\\\end{aligned}\)
Therefore, the slope is \(\dfrac{1}{4}\).
The point-slope form of the equation of a line with slope \(m\) passes through point \(\left({{x_1},{y_1}}\right)\) is represented as follows:
\(y - {y_1}=m\left({x - {x_1}}\right){\text{}}\) ......(2)
Substitute for \({x_1}\) , \(1\) for \({y_1}\) and \(\frac{1}{4}\) for \(m\) in equation (2) to obtain the equation of line.
\(\begin{aligned}y - 1&=\frac{1}{4}\left({x - 12}\right)\\4\left({y - 1}\right)&=x - 12\\4y - 4&=x - 12\\x - 4y&=8\\\end{aligned}\)
Therefore the standard equation of line that passes through points \(\left({ - 4, - 3}\right)\) and \(\left({12,1}\right)\) is \(x - 4y = 8\).
Thus, theequation of line passes through points \(\left({ - 4, - 3}\right)\) and \(\left({12,1}\right)\) in standard form is \(\boxed{{\mathbf{x - 4y = 8 }}}\)
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Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Coordinate Geometry
Keywords:Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics,equation of line, line, passes through point