Final answer:
To write the equation in standard form for the line passing through the given points (-2,-3) and (4,-7), we first find the slope using the formula (y2 - y1) / (x2 - x1). Then we substitute one of the points into the slope-intercept form y = mx + b to find the y-intercept. Finally, we rearrange the terms to obtain the equation 2x + 3y = -13 in standard form.
Step-by-step explanation:
To write an equation in standard form for the line that passes through the points (-2,-3) and (4,-7), we need to find the slope of the line. The slope, denoted as 'm', can be found using the formula: m = (y2 - y1) / (x2 - x1). So, plugging in the given points, we have m = (-7 - (-3)) / (4 - (-2)) = -4 / 6 = -2/3.
Next, we can use the slope-intercept form, y = mx + b, where 'm' is the slope and 'b' is the y-intercept, to find the equation. We can choose either of the given points to substitute for (x, y) in this equation. Let's use the first point (-2,-3): -3 = (-2/3)(-2) + b. Simplifying this equation gives us -3 = 4/3 + b. To solve for 'b', subtract 4/3 from both sides, giving b = -3 - 4/3 = -13/3.
Therefore, the equation in slope-intercept form is y = (-2/3)x - 13/3. To convert this to standard form, we can multiply both sides of the equation by 3 to eliminate the fraction, resulting in 3y = -2x - 13. Finally, rearranging the terms gives us the equation in standard form: 2x + 3y = -13.