SOLUTION
Step 1 :
In this question, we are expected to find the equation of the line,
y = m x + c
where y = dependent variable,
x = dependent variable,
m = gradient of the line
c = intercept on the y - axis.
Step 2 :
We are given that :
[tex]\begin{gathered} \text{The gradient of the line, } \\ m\text{ }=\text{ }\frac{y_2-y_1}{x_{2_{}}-x_1} \\ \text{where (x }_{1\text{ , }}y_{1\text{ }}\text{ ) = ( 4, 3)} \\ (x_{2\text{ , }}y_2\text{ ) = ( -4 ,- 3 )} \\ \text{Then we have that :} \\ m\text{ = }\frac{(\text{ -3 - 3 ) }}{-\text{ 4 - 4}} \\ m\text{ = }\frac{-6}{-8} \\ m\text{ =}\frac{3}{4} \end{gathered}[/tex]
Step 3 :
Since ( x 1, y 1) = ( 4, 3 ) and
[tex]\begin{gathered} \text{the gradient m = }\frac{3}{4}\text{. } \\ y-y_{1\text{ }}=m(x-x_1) \\ y\text{ - 3 =}\frac{3}{4}\text{ ( x - 4 )} \\ \text{simplifying further, we have that:} \\ 4\text{ y - 12 = 3 x - }12 \\ 4y\text{ - 3x - 12 + 12 = 0} \\ 4\text{ y - 3 x = 0} \\ \operatorname{Re}-\text{arranging the equation, we have that:} \\ 4\text{ y = 3 x } \end{gathered}[/tex]
CONCLUSION:
The final answer is :
[tex]y=\text{ }\frac{3}{4}\text{ x }[/tex]
