A teacher used the change of base formula to determine whether the equation below is correct.
1 answer:
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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](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%20%28a%2Cb%29%0A%26%28%7B%7B%20-3%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%5Cquad%20%0A%25%20%20%20%28c%2Cd%29%0A%26%28%7B%7B%20-4%7D%7D%5Cquad%20%2C%26%7B%7B%200%7D%7D%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20slope%20%20%3D%20m%0Aslope%20%3D%20%7B%7B%20m%7D%7D%3D%20%5Ccfrac%7Brise%7D%7Brun%7D%20%5Cimplies%20%0A%5Ccfrac%7B%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%7D%7B%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%7D%5Cimplies%20%5Ccfrac%7B0-2%7D%7B-4-%28-3%29%7D%5Cimplies%20%5Ccfrac%7B0-2%7D%7B-4%2B3%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B-2%7D%7B-1%7D%5Cimplies%202%0A%5C%5C%5C%5C%5C%5C%0A%25%20point-slope%20intercept%0A%5Cstackrel%7B%5Ctextit%7Bpoint-slope%20form%7D%7D%7By-%7B%7B%20y_1%7D%7D%3D%7B%7B%20m%7D%7D%28x-%7B%7B%20x_1%7D%7D%29%7D%5Cimplies%20y-2%3D2%5Bx-%28-3%29%5D%0A%5C%5C%5C%5C%5C%5C%0Ay-2%3D2%28x%2B3%29%5Cimplies%20y-2%3D2x%2B6%5Cimplies%20y%3D2x%2B8)
so, what's the equation of a line that passes through (-3,2) and (-4,0)?