Write an equation of the line passing through $(-2,3)$ and $(6,4)$. Give the answer in standard form.
The equation of the line in standard form is

Step 1 ：Given two points (-2,3) and (6,4), we can find the equation of the line passing through these points.

Step 2 ：First, we calculate the slope of the line using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting the given points into the formula, we get \(m = \frac{4 - 3}{6 - (-2)} = 0.125\).

Step 3 ：Next, we use the slope and one of the points to find the y-intercept, b, using the formula \(b = y - mx\). Substituting the point (-2,3) and the slope into the formula, we get \(b = 3 - 0.125*(-2) = 3.25\).

Step 4 ：So, the equation of the line in slope-intercept form is \(y = 0.125x + 3.25\).

Step 5 ：We want the equation in standard form, which is \(Ax + By = C\). We can convert the slope-intercept form to standard form by rearranging the equation to get \(-0.125x + y = 3.25\).

Step 6 ：However, it is more common to see the standard form with integer coefficients. We can achieve this by multiplying the entire equation by 8 to get \(-x + 8y = 26\).

Step 7 ：Final Answer: The standard form of the line passing through (-2,3) and (6,4) is \(\boxed{-x + 8y = 26}\).