Find an equation for the line with the given properties. Perpendicular to the line -2x+3y=-1;y-intercept=4

To find the equation of a line that is **perpendicular** to the given line and has a **y-intercept** of 4, follow these steps:---### Step 1: Find the slope of the given lineThe general form of a line is . To determine the slope of the given line, rewrite it in slope-intercept form ( ), where is the slope.Start with: Solve for : Thus, the slope of the given line is: ---### Step 2: Find the slope of the perpendicular lineThe slopes of two perpendicular lines are negative reciprocals of each other. If the slope of one line is , then the slope of the perpendicular line is: Substitute : So, the slope of the perpendicular line is: ---### Step 3: Write the equation of the perpendicular lineWe are told that the y-intercept of the desired line is 4. The slope-intercept form of a line is: where is the slope and is the y-intercept.Substitute and : ---### Final Answer:The equation of the line is: