Answer:
The equation in slope-intercept form is;
[tex]y = -\dfrac{1}{4} \cdot x + 4\frac{3}{4}[/tex]
Step-by-step explanation:
The equation of a straight line in slope and intercept form is given as follows;
y = m·x + c
Where;
m = The slope of the line
c = The y-intercept of the line
The points through which the line passes are;
(7, 3) and (-1, 5), therefore, the slope of the line, m, is given as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where (x₁, y₁) = (7, 3) and (x₂, y₂) = (-1, 5), we have;
[tex]Slope, \, m =\dfrac{5-3}{(-1)-7} = -\dfrac{1}{4}[/tex]
Therefore;
[tex]\dfrac{y-3}{x-7} = -\dfrac{1}{4}[/tex]
The equation in point slope form is therefore;
[tex]y - 3 = -\dfrac{1}{4} \times (x - 7)[/tex]
From which we have;
y - 3 = -1/4×(x - 7) = -x/4 + 7/4
y = -x/4 + 7/4 + 3 = -x/4 + 19/4
The equation in slope-intercept form is therefore;
[tex]y = -\dfrac{1}{4} \cdot x + 4\frac{3}{4}[/tex]
Which can be expressed as follows
y = -0.25·x + 4.75.
