Question 568796
{{{y =(3/4)x + 7}}} is the equation of a line in slope-intercept form
That form starts with "y=", has the y-intercept for a constant/independent term, and has the slope for coefficient of the {{{x}}}. The slope is {{{3/4}}} in this case.
{{{2x + 4y = 8}}}
Solving for {{{y}}}, we get the slope intercept form
{{{2x + 4y = 8}}} --> {{{2x + 4y -2x = 8-2x}}} --> {{{4y=-2x+8}}} --> {{{4y/4=(-2x+8)/4}}} --> {{{y=-2x/4+8/4}}} --> {{{y=-(1/2)x+2}}}
The slope is {{{-1/2}}}
{{{5.1476x + 5.1476 = 15}}} I suspect a typo, but if it was really written like that, it is really
{{{5.1476x + 5.1476 = 15}}} --> {{{5.1476x = 15-5.1476 }}} --> {{{5.1476x=9.8524 }}} --> {{{x=9.8524/5.1476}}}
Without doing that division we see that {{{x}}} is constant, while {{{y}}} could be anything. There is no slope. The slope is undefined, and the line is a vertical line.
{{{y - 3 = (7/13)(x-4)}}} is the equation in point-slope form of the line with slope {{{7/13}}} that passes through the point (4,3).
{{{y - 7.3591 = (7/13)(x-4.0856)}}} is the equation in point-slope form of the line with slope {{{7/13}}} that passes through the point (4.0856,7.3591).