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Vlada [557]
3 years ago
13

Find the slope and the equation for the line passing through the (-3,2 ) point with x-intercept at x=-4. and how do I find the e

quation of this line
Mathematics
1 answer:
WINSTONCH [101]3 years ago
3 0
Well, the x-intercept is at -4, that means, the graph touches the x-axis at -4, or when x = -4, what's the value of "y" when that happens?  well, if the graph touches the x-axis, the y-value has gone all the way down to 0, and thus y = 0, therefore the point at that x-intercept is ( -4, 0 )

so, what's the equation of a line that passes through (-3,2) and (-4,0)?

\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
&({{ -3}}\quad ,&{{ 2}})\quad 
%   (c,d)
&({{ -4}}\quad ,&{{ 0}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{0-2}{-4-(-3)}\implies \cfrac{0-2}{-4+3}
\\\\\\
\cfrac{-2}{-1}\implies 2
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=2[x-(-3)]
\\\\\\
y-2=2(x+3)\implies y-2=2x+6\implies y=2x+8
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