Question 1158144
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We are given a point and the slope, so we use the point slope form
for an equation of a line:

{{{matrix(1,3,y-y[1],""="",m(x-x[1]))}}}

where we substitute the given slope for m and the given point for (x<sub>1</sub),y<sub>1</sub>).  
[We do not substitute for x and y, but leave them variable.]

{{{matrix(1,3,y-5,""="",expr(4/3)(x-3))}}}

Distribute the 4/3:

{{{matrix(1,3,y-5,""="",expr(4/3)x-4)}}}

Add 5 to both sides

{{{matrix(1,3,y,""="",expr(4/3)x+1))}}}

Now it's in the slope-y-intercept form where the slope is 4/3 and the
y-intercept is 1

We'll check the choices:</pre>The y-intercept is 4.<pre>That's wrong because the y-intercept is 1, not 4.</pre>The slope-intercept equation is y = four-thirds x + 1.<pre>That's true because that's what we got.  So we have the answer. 
But let's see why the others are false anyway.</pre>The point-slope equation is y minus 3 = four-thirds (x minus 5).<pre>That's wrong because that has the x<sub>1</sub> and y<sub>1</sub> switched.</pre>The line also passes through the point (0,  -  2).<pre>Let's substitute that and see why it's false:

{{{matrix(1,3,y,""="",expr(4/3)x+1))}}}
{{{matrix(1,3,-2,""="",expr(4/3)0+1))}}}
{{{matrix(1,3,-2,""="",0+1))}}}
{{{matrix(1,3,-2,""="",1))}}}

That's certainly false.

Edwin</pre>