Answer:
A linear function in the form y = m·x + b for the line passing through the point (2, -4) with y-intercept 2 is;
y = -3·x + 2
Step-by-step explanation:
From the question, it is required to find the a linear equation passing through the point (2, - 4) with a y-intercept 2 in the form y = m·x + c
Given that the y-intercept is the point at which the line cuts the y-axis, we have, x = 0
Therefore, we have the point on the line representing the y-intercept is (0, 2)
Therefore, the slope of the graph is given as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Therefore, we have;
[tex]Slope, \, m =\dfrac{2-(-4)}{0-2} = \dfrac{6}{-2} = -3[/tex]
The equation of the graph in point and slope is given as follows;
y - 2 = -3 × (x - 0) = -3 × x
Therefore, the equation of the line in the form y = m·x + c is given as follows;
y - 2 + 2 = -3 × x + 2
∴ y = -3·x + 2
The equation of the line in the form y = m·x + c is y = -3·x + 2.