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Answer:
x-intercept: [tex]\bigg(\frac{5}{2}, \:0\bigg)[/tex]
y-intercept: [tex](0,\:5)[/tex]
Step-by-step explanation:
To find the x-intercept, substitute in [tex]0[/tex] for [tex]y[/tex] and solve for [tex]x[/tex].
[tex]-4x + 7 = 2y - 3[/tex]
[tex]-4x+7=2\left(\bold{0}\right)-3[/tex]
Simplify 2(0): [tex]-4x+7=2\cdot \:0-3[/tex]
Subtract 0 - 3 = -3: [tex]-4x+7=-3[/tex]
Subtract 7 from both sides: [tex]-4x+7-7=-3-7[/tex]
Simplify: [tex]-4x=-10[/tex]
Divide both sides by -4 [tex]\frac{-4x}{-4}=\frac{-10}{-4}[/tex]
[tex]\bold{x=\frac{5}{2}}[/tex]
To find the y-intercept, substitute in [tex]0[/tex] for [tex]x[/tex] and solve for [tex]y[/tex].
[tex]-4x + 7 = 2y - 3[/tex]
[tex]-4(\bold{0})+7=2y-3[/tex]
Switch sides: [tex]y-3=-4\left(0\right)+7[/tex]
Simplify -4(0): [tex]2y-3=-0+7[/tex]
Add 3 to both sides: [tex]2y-3+3=7+3[/tex]
Simplify: [tex]2y=10[/tex]
Divide both sides by 2: [tex]\frac{2y}{2}=\frac{10}{2}[/tex]
[tex]\bold{y=5}[/tex]