Answer:
y = [tex]\frac{5}{4}[/tex] x + 12
Step-by-step explanation:
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 5x - 4y = 4 into this form
subtract 5x from both sides
- 4y = - 5x + 4 ( divide all terms by - 4 )
y = [tex]\frac{5}{4}[/tex] x - 1 ← in slope-intercept form
with slope m = [tex]\frac{5}{4}[/tex]
• Parallel lines have equal slopes, hence
y = [tex]\frac{5}{4}[/tex] x + c ← is the partial equation
to find c substitute (- 8, 2 ) into the partial equation
2 = - 10 + c ⇒ c = 2 + 10 = 12
y = [tex]\frac{5}{4}[/tex] x + 12 ← equation of parallel line
The equation passing through the point (-8, 2) and parallel to 5x - 4y = 4 is
y = 5/4 x + 12
The given equation is:
5x - 4y = 4
Rewrite the equation 5x - 4y = 4 in the form y = mx + c
4y = 5x - 4
y = 5/4 x - 4/4
y = 5/4 x - 1
where the slope, m = 5/4 and the intercept, c = -1
The equation of a line is of the form:
y - y₁ = m(x - x₁)
The line passes through the point (-8, 2)
That is, x₁ = -8, y₁ = 2
Substitute x₁ = -8 and y₁ = 2 into the equation y - y₁ = m(x - x₁)
y - 2 = 5/4 ( x - -8)
y - 2 = 5/4 (x + 8)
y = 5/4 x + 8(5/4) + 2
y = 5/4 x + 10 + 2
y = 5/4 x + 12
The equation passing through the point (-8, 2) and parallel to 5x - 4y = 4 is
y = 5/4 x + 12
Learn more here: https://brainly.com/question/11552995
