Question 154404
<h4>X-Intercept</h4>



To find the x-intercept, plug in {{{y=0}}} and solve for x



{{{y=4x-2}}} Start with the given equation.



{{{0=4x-2}}} Plug in {{{y=0}}}.



{{{2=4x}}} Add {{{2}}} to both sides.



{{{(2)/(4)=x}}} Divide both sides by {{{4}}} to isolate {{{x}}}.



{{{1/2=x}}} Reduce.



So when {{{y=0}}} then {{{x=1/2}}}



This means that the x-intercept is *[Tex \LARGE \left(\frac{1}{2},0\right)].



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<h4>Y-Intercept</h4>



To find the y-intercept, plug in {{{x=0}}} and solve for y



{{{y=4x-2}}} Start with the given equation.



{{{y=4(0)-2}}} Plug in {{{x=0}}}.



{{{y=0-2}}} Multiply {{{4}}} and 0 to get 0.



{{{y=-2}}} Subtract




So when {{{x=0}}} then {{{y=-2}}}





This means that the y-intercept is *[Tex \LARGE \left(0,-2\right)].




Now graph the x and y intercepts as points in a coordinate system:




{{{ drawing(500, 500, -5, 5, -5, 5,
grid(1),
graph(500, 500, -5, 5, -5, 5,0),
circle(0,-2,0.05),
circle(0,-2,0.08),
circle(0,-2,0.10),

circle(0.5,0,0.05),
circle(0.5,0,0.08),
circle(0.5,0,0.10)

)}}} Graph of the x-intercept *[Tex \LARGE \left(\frac{1}{2},0\right)] and the y-intercept *[Tex \LARGE \left(0,-2\right)].




Now draw a line through the two points to graph {{{y=4x-2}}}



{{{ drawing(500, 500, -5, 5, -5, 5,
graph(500, 500, -5, 5, -5, 5,4x-2),
grid(1),
circle(0,-2,0.05),
circle(0,-2,0.08),
circle(0,-2,0.10),

circle(0.5,0,0.05),
circle(0.5,0,0.08),
circle(0.5,0,0.10)
)}}} Graph of {{{y=4x-2}}}