Alejandra correctly wrote the equation y-3=(1)/(5)(x-10) to represent a line that her teacher sketched.The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line? y-6=2(x-10) y-2=(1)/(5)(x-10) y-3=(1)/(5)(x-2) y-3=2(x-10)

## Step 1<br />The problem involves the concept of linear equations in two variables, specifically the slope-intercept form of a linear equation. The slope-intercept form of a linear equation is given by:<br />### \(y - y_1 = m(x - x_1)\)<br />where \(m\) is the slope of the line and \((x_1, y_1)\) is a point on the line.<br /><br />## Step 2<br />In the given equation \(y - 3 = \frac{1}{5}(x - 10)\), the slope \(m\) is \(\frac{1}{5}\) and the point \((x_1, y_1)\) is \((10, 3)\).<br /><br />## Step 3<br />The teacher changes the slope of the line to 2, but the line still passes through the same point \((10, 3)\). Therefore, the new equation of the line should have the same point \((10, 3)\) and the new slope \(m = 2\).<br /><br />## Step 4<br />Substituting the new slope and the point into the slope-intercept form, we get:<br />### \(y - 3 = 2(x - 10)\)